Variable impedance circuit

ABSTRACT

A variable impedance circuit includes a first differential amplifier circuit having an input terminal pair, an output terminal pair and a capacitive element connected between the emitters of a transistor pair. The variable impedance circuit further inclludes a second differential amplifier circuit having an input terminal pair and an output terminal pair. The output terminal pair of the first differential amplifier circuit is connected to the input terminal pair of the second differential amplifier circuit. Furthermore, the output terminal pair of the second differential amplifier circuit is connected to the input terminal pair of the first differential amplifier circuit.

BACKGROUND OF THE INVENTION

This invention relates to a variable impedance circuit capable ofelectrically increasing or decreasing the impedance, such as resistanceand capacitance.

Recently, the function of semiconductor integrated circuits has beengreatly improved, and the filter circuit has come to be incorporated ina semiconductor chip as an integrated circuit. Generally a filtercircuit is composed of a resistance element and a capacitance element.To change the filtering characteristic of the filter circuit, it isnecessary to vary the value of constituent elements, that is, thecapacitance element or the resistance element. Accordingly, hitherto, avariable impedance circuit has been used, which can vary the value ofcapacitance element or resistance element built in a semiconductor chip.

FIG. 12 shows a conventional variable capacitance circuit used for sucha purpose, expressed only by an AC circuit. In FIG. 13, the variablecapacitance circuit in FIG. 12 is expressed by both an AC circuit and DCcircuit.

In FIG. 12 and FIG. 13, a differential amplifier circuit 15 is composedof transistors Q₅, Q₆, and a resistance element 10 connected betweentheir emitters. A differential amplifier circuit 16 is composed oftransistors Q₇, Q₈, and a resistance element 11 connected between theiremitters. A differential amplifier circuit 17 is composed of transistorsQ₁, Q₂, and a resistance element 12 connected between their emitters. Adifferential amplifier circuit 18 is composed of transistors Q₃, Q₄, anda resistance element 13 connected between their emitters. As is clearfrom FIG. 12 and FIG. 13, the differential amplifier circuits 15, 16 areso connected that the input terminals of one differential amplifiercircuit are connected to the output terminals of the other differentialamplifier circuit. The differential amplifier circuits 17, 18 are alsoconnected in a similar relation. These differential amplifier circuits15, 16, 17 and 18 are connected as shown in FIG. 12, FIG. 13, and acapacitance element 14 is connected between two output terminals of thedifferential amplifier circuit 17. The transistors Q₁ to Q₈ forcomposing the differential amplifier circuits 15, 16, 17 and 18 aresupplied with biases from voltage sources V₀, V₁, and constant currentsource I₀ as shown in FIG. 13.

The voltage-current conversion factors of the differential amplifiercircuits 15, 16, 17 and 18 are determined respectively by thecharacteristics of the resistance elements 10, 11, 12 and 13.

The operation is explained below.

The relation

    i.sub.2 =g.sub.1 ·V.sub.1                         ( 1)

is established between voltage V₁ and output current i₂ across inputterminals of the differential amplifier circuit 17. In this equation g₁denotes the voltage-current conversion factor of the differentialamplifier circuit 17, and supposing the emitter resistance value oftransistors Q₁, Q₂ to be r_(el), and the value of resistance element 12between emitters to be R₁, g₁ it is expressed as follows. ##EQU1##

The characteristics of voltage V₂ and current i₂ occurring at both endsof the capacitance element 14 of capacitance value C₀ are obtained asfollows.

    i.sub.2 =-jωC.sub.0 ·V.sub.2                ( 3)

Similarly, the characteristics of voltage V₂ across input terminals andoutput current i₁ of the differential amplifier circuit 18 composed oftransistors Q₃, Q₄ are obtained as follows:

    i.sub.1 =-g.sub.2 ·V.sub.2                        ( 4)

where g₂ denotes the voltage-current conversion factor of thedifferential amplifier circuit 18, and supposing the resistance value ofeach emitter of transistors Q₃, Q₄ to be r_(e2), and the value of theresistance element 13 between the emitters to be R₂, g₂ is expressed asfollows. ##EQU2##

Solving V₁ and i₁ from equations (1), (3) and (4), it is known fromequations (1), (3) that ##EQU3## and from equations (4), (6) that##EQU4##

That is, ##EQU5##

Here, the inductance L is given as follows. ##EQU6##

Furthermore, from equations (2), (5), it follows that

    L=(R.sub.1 +2r.sub.el)(R.sub.2 +2r.sub.e2)C.sub.0          ( 10)

Usually, the resistance values can be set so as to establish therelation of R₁ >r_(el), R₂ >r_(e2), and hence the inductance L can beapproximated as

    L=R.sub.1 ·R.sub.2 ·C.sub.0

Likewise, the characteristics of input terminal voltage V₃ and outputcurrent i₄ of the differential amplifier circuit 15 composed oftransistors Q₅, Q₆ may be expressed as follows, supposing thevoltage-current conversion factor of the differential amplifier circuit15 to be g₃ :

    i.sub.4 =g.sub.3 ·V.sub.3                         ( 11)

Supposing the voltage-current conversion factor of the differentialamplifier circuit 16 to be g₄, the characteristics of input terminalvoltage V₄ and output current i₃ of the differential amplifier 16composed of transistors Q₇, Q₈ are as follows.

    i.sub.3 =-g.sub.4 ·V.sub.4                        ( 12)

The circuit systems respectively composed of the differential amplifiercircuits 15, 16, and the differential amplifier circuits 17, 18represent the conventionally used phase conversion circuits. The circuitsystem composed of the differential amplifiers 17, 18 is designed toapply from capacitance characteristics to inductance characteristics, interms of circuitry.

In FIG. 12 and FIG. 13, the relations

    V.sub.4 =V.sub.1                                           ( 13)

    i.sub.4 =-i.sub.1                                          ( 14)

are established between the voltages V₁, V₄, and currents i₄, i₁,respectively. Hence, equation (8) is rewritten as ##EQU7## and furtherby eliminating i₄ from equation (11), it results in ##EQU8## and fromequations (16) and (12), it follows that ##EQU9##

The capacitance value C applied between the voltage V₃ and current i₃ isgiven as ##EQU10## That is, by properly selecting the values for thevoltage-current conversion factors g₁, g₂, g₃ and g₄, the capacity valueC is newly created electrically.

However, in the conventional variable capacitance circuit shown in FIG.12, FIG. 13, at least four differential amplifier circuits are needed inorder to obtain a new capacitance value by electrically increasing ordecreasing the capacitance. Accordingly, the circuit composition iscomplicated, the number of required elements increases, and the chiparea increases.

A conventional variable resistance circuit incorporated in asemiconductor chip is explained below while referring to FIG. 14.

In FIG. 14, transistors 41, 42 are connected between a constant voltagesource 40 and the grounding potential. A constant voltage source 43 isconnected to the base of the transistor 41. A variable voltage source 44is connected to the base of the transistor 42. An output terminal 45 isconnected to the connecting points of the transistors 41, 42.

In the structure in FIG. 14, the resistance value as seen from theoutput terminal 45 is equal to the differential emitter resistance ofthe transistor 41 (that is, the impedance of the transistor 41 seen fromits emitter), and it is given in the following formula. ##EQU11## wherek is Boltzmann constant, T is absolute temperature, q is electric chargequantity of an electron, and I₀ is emitter current flowing in thetransistor 41. When the voltage of the variable voltage source 44 isvaried, the current I₀ changes, and hence the resistance value as seenfrom the output terminal 45 varies. Therefore, by controlling thevoltage of the variable voltage source 44, a variable resistance may beobtained.

However, in the conventional variable resistance circuit shown in FIG.14, since the differential emitter resistance itself of the transistor41 is used as a variable resistance component, the variable range of theresistance value is narrow.

SUMMARY OF THE INVENTION

It is hence a first object of the invention to present a variableimpedance circuit capable of varying the impedance, such as capacitancevalue and resistance value, by using two differential amplifiercircuits.

It is a second object of the invention to present a variable impedancecircuit capable of widening the variable range of impedance, such ascapacitance value and resistance value.

The invention is, in short, intended to obtain a new impedance from thevoltage and current characteristics caused between the pair of inputterminals of a first differential amplifier circuit, by connecting theoutput terminal pair of the first differential amplifier circuit to theinput terminal pair of a second differential amplifier circuit,connecting the output terminal pair of the second differential amplifiercirucuit to the input terminal pair of the first differential amplifiercircuit, and connecting an impedance element such as capacitance elementor resistance element between the emitters of the transistor paircomposing the first differential amplifier circuit.

In this way, the variable impedance circuit is composed of twodifferential amplifier circuits, and the circuit composition may besimplified, and the number of required elements is smaller. Therefore,when this variable impedance circuit is incorporated in a semiconductorchip, the required chip area may become small. Moreover, as comparedwith the prior art in which differential emitter resistance is directlyused as variable resistance component, the variable range of theimpedance may become greater.

BRIEF DESCRIPTION OF THE DRAWINGS

FIG. 1 is a circuit diagram expressing a variable impedance circuit in afirst embodiment of the invention only by an AC circuit,

FIG. 2 is a circuit diagram expressing the first embodiment by both anAC circuit and DC circuit,

FIG. 3 is a circuit diagram expressing a variable impedance circuit in asecond embodiment of the invention only by an AC circuit,

FIG. 4 is a circuit diagram expressing the second embodiment by both anAC circuit and DC circuit,

FIG. 5 is a circuit diagram expressing a variable impedance circuit in athird embodiment of the invention only by an AC circuit,

FIG. 6 is a circuit diagram expressing the third embodiment by both anAC circuit and DC circuit,

FIG. 7 is a circuit diagram expressing a variable impedance circuit in afourth embodiment of the invention only by an AC circuit,

FIG. 8 is a circuit diagram expressing the fifth embodiment by both anAC circuit and DC circuit,

FIG. 9 is a circuit diagram of a variable impedance circuit in a sixthembodiment of the invention modified from the embodiment shown in FIG.2, expressed by both an AC circuit and DC circuit,

FIG. 10 is a circuit diagram expressing a variable impedance circuit ina seventh embodiment of the invention by both an AC circuit and DCcircuit,

FIG. 11 is a circuit diagram expressing a variable impedance circuit inan eighth embodiment of the invention by both an AC circuit and DCcircuit,

FIG. 12 is a circuit diagram expressing a conventional variable capacitycircuit only by an AC circuit,

FIG. 13 is a circuit diagram expressing the conventional variablecapacity circuit shown in FIG. 12 by both an AC circuit and DC circuit,and

FIG. 14 is a circuit diagram showing a conventional variable resistancecircuit.

DETAILED DESCRIPTION OF THE INVENTION

Referring now to FIG. 1 and FIG. 2, a first embodiment of the inventionis described in detail below.

In FIG. 1, FIG. 2, a differential amplifier 1 is composed of transistorsQ₁, Q₂, and a capacitance element 3 connected between their emitters. Adifferential amplifier circuit 2 is composed of transistors Q₃, Q₄, anda resistance element 5 connected between their emitters. The outputterminal pair of the differential amplifier circuit 1 is connected tothe input terminal pair of the differential amplifier circuit 2. Theoutput terminal pair of the differential amplifier circuit 2 isconnected to the input terminal pair of the differential amplifiercircuit 1. A resistance element 6 is connected between the inputterminals of the differential amplifier circuit 2. Biases are suppliedto the transistors Q₁ to Q₄ from voltage source V₁, and constant currentsources I₀, I₁.

The operation is explained below.

Supposing the input terminal AC voltage of the differential amplifiercircuit 1 to be V₁, and the voltage-current conversion factor of thedifferential amplifier circuit 1 to be g_(m1), the output AC current i₂is given as

    i.sub.2 =g.sub.m1 ·V.sub.1                        (19)

The voltage V₂ produced between the both ends of the resistance element6 of which resistance value is R₃ is given as

    V.sub.2 =-i.sub.2 ·R.sub.3                        (20)

Supposing the voltage-current conversion factor of the differentialamplifier circuit 2 to be g_(m2), the output current i₁ flowing due tothe voltage V₂ applied between the input terminals of the differentialamplifier circuit 2 is given as

    i.sub.1 =-g.sub.m2 ·V.sub.2                       (21)

From equations (19), (20), it follows that

    V.sub.2 =-g.sub.m1 ·R.sub.3 ·V.sub.1     (22)

From equations (22), (21), it follows that

    i.sub.1 =g.sub.m1 ·g.sub.m2 ·R.sub.3 ·V.sub.1(23)

Here, the voltage-current conversion factor g_(m2) of the differentialamplifier circuit 2 is given by the resistance characteristic. In otherwords, the voltage-current conversion factor g_(m2) is determined by theemitter resistance value r_(e2) of transistors Q₃, Q₄ and the resistancevalue R₂ of the resistance element 5, and is obtained as follows.##EQU12## Supposing here r_(e2) <<R₂, it follows that ##EQU13##

Next, the voltage-current conversion factor g_(m1) of the differentialamplifier circuit 1 is given by the characteristics of the capacitanceelement 3. Here, the voltage-current conversion factor g_(m1) is givenby the impedance of the capacitance element 3 ##EQU14## and the emitterresistance value r_(e1) of the transistors Q₁, Q₂, and it becomes##EQU15## Here, if selecting as 2r_(e1) <<|Z|, it follows that ##EQU16##Putting equations (24), (26) into equation (23) yields ##EQU17## As aresult, between the voltage V₁ and current i₁, a new capacitance value Cis given as ##EQU18## By selecting the ratio of the resistance value R₃and R₂, another new capacitance value C may be obtained from theoriginal capacitance value C₁.

Furthermore, as seen from equation (23), it is enough when thecapacitance characteristic is given to either one of the voltage-currentconversion factor g_(m1) or g_(m2).

FIG. 3 and FIG. 4 relate to a second embodiment of the invention. Thevariable impedance circuit shown in FIG. 3, FIG. 4 comprisesdifferential amplifier circuits 8, 9, and a resistance element 7 isconnected between the emitters of transistors Q₁, Q₂ for composing thedifferential amplifier circuit 8, and a capacitance element 4 isconnected between the emitters of transistors Q₃, Q₄ for composing thedifferential amplifier circuit 9. The remaining composition is the sameas in the first embodiment shown in FIG. 1, FIG. 2.

Now, assuming the capacitance value of the capacitance element 4 to beC₂ and the resistance value of the reistance element 7 to be R₁,equations (26), (24) in the first embodiment are respectively rewrittenas ##EQU19## and the current i₁ becomes ##EQU20## That is, same as inthe first embodiment, a new capacitance value C is applied between thevoltage V₁ and current i₁ as ##EQU21## Therefore, by selecting the ratioof the resistance value R₃ and R₁, a new capacitance value C may beobtained from the initial capacity value C₂.

FIG. 5 and FIG. 6 relate to a third embodiment of the invention. In thisembodiment, as clearly seen from FIG. 5, the output terminal pair of thedifferential amplifier circuit 2 is connected to the input terminal pairof the differential amplifier circuit 1 by way of a current-currentconversion circuit 20. The current-current conversion circuit 20 may berealized, for example as shown in FIG. 6, by a known Gilbertmultiplication circuit composed of transistors Q₅ to Q₈, and currentsource 2I₂. Meanwhile, to the transistors Q₇, Q₈ of the current-currentconversion circuit 20, a base bias is applied from a voltage source V₂.The remaining composition is substantially the same as shown in FIG. 2,FIG. 4.

When such current-current conversion circuit 20 is used, the currentvalue of the differential amplifier circuit 2 may be variedindependently of the composition of the differential amplifier circuit2. In other words, supposing there is a coefficient K for convertingcurrent i₁ into other current i₁ ', the relation is

    i.sub.1 '=K·i.sub.1                               (32)

Putting equation (32) into equation (27), the converted current i₁ ' isexpressed as ##EQU22## Therefore, the capacitance value C' afterconversion is ##EQU23##

As known from equation (34), the new capacitance value C' may beincreased or decreased by the quantity given as the product of K and R₃/R₂. Since K is determined by I₂ /I₀, equation (34) is finally rewrittenas ##EQU24## That is, according to the embodiment shown in FIG. 6, thecapacitance value can be changed not only by the ratio of resistancecomponents (R₃ /R₂), but also by the ratio of current components (I₂/I₀). Therefore, a greater capacitance value may be obtained.

FIG. 7 shows a fourth embodiment of the invention, having acurrent-current conversion circuit 20 added to the embodiment in FIG. 3.In FIG. 7, the current value of the differential amplifier circuit 9 mayalso be varied independently of the composition of the differentialamplifier circuit 9. In FIG. 7, the capacitance value C' afterconversion is given as ##EQU25##

When the current-current conversion circuit 20 is used as shown in theembodiments in FIG. 5 to FIG. 7, the following advantages are broughtabout. Since the resistance element and capacitance element of thevariable impedance circuit of the invention are formed in asemiconductor chip, their values are fixed. However, when actuallycomposing a filter circuit by using this variable impedance circuit, itmay be sometimes desired to vary the frequency characteristics of thefilter only very slightly. In such a case, by using the current-currentconversion circuit 20, the filter circuit may be furnished with a kindof a variable resistor function, so that a desired frequencycharacteristic may be realized quite easily.

FIG. 8 shows a fifth embodiment of the invention modifying theembodiment shown in FIG. 6. That is, instead of the linear resistanceelements 6, 6 in FIG. 6, nonlinear characteristic resistances 21, 21composed of transistors Q₉, Q₁₀ are used, and a base bias is applied tothese transistors Q₉, Q₁₀ from a voltage source V₂. Meanwhile, in thecomposition in FIG. 8, a resistance element is not connected between theemitters of the transistors Q₃, Q₄ for composing a differentialamplifier circuit 22.

In the embodiment shown in FIG. 8, the transistors Q₉, Q₁₀, thetransistors Q₃, Q₄ for composing the differential amplifier circuit 22,and the current source 2I₀ fulfill substantially an equivalentcurrent-current converting function as the Gilbert multiplicationcircuit 20 shown in FIG. 6. Accordingly, the current-current convertingfunction is realized in a simple circuit structure. Moreover, whencomposed as shown in FIG. 8, since the base potentials of thetransistors Q₉, Q₁₀ are fixed by the potential of the voltage source V₂,the emitter potentials of the transistors Q₃, Q₄ for composing thedifferential amplifier circuit 22 are also fixed nearly at specificpotentials. Therefore, particularly when the supply voltage is small,the circuit design becomes quite easy, and the dynamic range of thetransistors Q₁, Q₂ for composing the differential amplifier circuit 1may be increased.

FIG. 9 shows a sixth embodiment shown of the invention, improving theembodiment in FIG. 2. Instead of the transistor Q₁ in FIG. 2, anoperational amplifier 24 is used, and instead of transistor Q₂ in FIG.2, an operational amplifier 25 is used. The operational amplifier 24 iscomposed of transistors Q₁₁ to Q₁₄, Q₁₉, and a current source I₃, whilethe operational amplifier 25 is composed of transistors Q₁₅ to Q₁₈, Q₂₀,and a current source I₃.

By thus composing, the emitter resistances of the transistors Q₁₉, Q₂₀become smaller in reverse proportion to the open gain of the operationalamplifiers 24, 25. As a result, the resistance component added seriallyto the capacitance element 3 is decreased.

FIG. 10 shows an embodiment shown of the invention applied to a variableresistance circuit.

The embodiment in FIG. 10 is a modified version of the composition ofFIG. 8, and the same parts are identified with the same referencenumbers and repeated explanations are omitted. A transistor Q₂₁ and avariable voltage source V₃ make up a current source, and an electriccurrent I_(x) is supplied into the differential amplifier circuit 2. Onthe other hand, resistance element 26, 27 are connected in seriesbetween the emitters of the transistors Q₁, Q₂ for composing thedifferential amplifier circuit 1, and a constant current source 28 isconnected between their connecting point and the reference potential.

Supposing the current flowing in the constant current source 28 to beI₀, the differential emitter resistance r_(eN) of the transistros Q₁,Q₂, Q₉ and Q₁₀ is an expressed as follows:

    r.sub.eN =(KT/q)/(I.sub.0 /2)                              (36)

where K is Boltzmann's constant, T is absolute temperature, and q iselectric charge quantity of an electron. The potentials applied to inputterminals 29 and 30 are supposed to be V₄ and V₅. When the potentials V₄and V₅ are changed, the emitter current flowing in the transistors Q₁and Q₂ varies. At the same time, the emitter current flowing in thetransistors Q₉ and Q₁₀ varies, and accordingly the potentials V₆ and V₇of the emitters of the transistors Q₉ and Q₁₀ are also changed. At thistime, the rate of change of voltage (V₇ -V₆) to the voltage (V₄ -V₅),that is, the voltage amplification factor G_(N) is given in thefollowing equation:

    G.sub.N =d(V.sub.6 -V.sub.7)/d(V.sub.4 -V.sub.5)=r.sub.eN /(r.sub.eN +R)(37)

where R is the resistance value of resistance elements 26 and 27, and itfunctions to increase the emitter series resistance of the transistorsQ₉ and Q₁₀. Supposing the collector current of the transistor Q₂₁ to beI_(x), each emitter current and collector current of the transistors Q₃and Q₄ are I_(x) /2. Therefore, the differential emitter resistancer_(ep) of the transistors Q₃ and Q₄ is given as follows:

    r.sub.er =(KT/q)/(I.sub.x /2)                              (38)

At this time, when the current value flowing in the constant currentsources 31 and 32 is set at I_(x) /2, the current flowing in from theinput terminals 29 and 30 becomes zero, which is very convenient. Therate of change of collector currents of the transistors Q₃ and Q₄ by thechange of the voltage (V₇ -V₆) generated between the bases of thetransistors Q₃ and Q₄, that is, the voltage-current conversion factor(mutual conductance) g_(mp) is given as follows.

    g.sub.mp =1/r.sub.ep                                       (39)

The change of the collector current of transistors Q₃ and Q₄ is equal tothe change of the currents I₁ and I₂ flowing in from the input terminals29 and 30. Therefore, the rate of change of currents I₁ and I₂ by thechanges of the potentials V₄ and V₅, d(I₁ -I₂)/d(V₄ -V₅), is given asfollows. ##EQU26## Futhermore, since the change of current I₁ and changeof current i₂ are equal to each other, the resistance value seen fromthe input terminals 29 and 30, d(V₄ -V₅)/dI₁ is expressed as follows.##EQU27## As known from the equation (41), the value of the resistanceis equal to the product of the differential emitter resistance r_(ep) oftransistors Q₃ and Q₄ multiplied by the coefficient {2(r_(eN) +R)/r_(eN)}. Here, since the resistance value R of the resistances 26 and 27 is apositive value, the coefficient {2(r_(eN) +R)/r_(eN) } is greater than2. To change the resistance value seen from the input terminals 29 and30, meanwhile, the voltage value of the variable voltage source V₃ ischanged and the collector current I_(x) of the transistor Q₂₁ ischanged, thereby varying vary the differential emitter resistancer_(ep).

According to the embodiment shown in FIG. 10, as compared with thevariation width of the differential emitter resistance r_(ep), theresistance value can be varied in a by more than twice the range.

In the embodiment shown in FIG. 10, meanwhile, the collector of thetransistor Q₃ is connected to the base of the transistor Q₂, and thecollector of the transistor Q₄ is connected to the base of thetransistor Q₁, but instead the collectors of the transistors Q₃ and Q₄may be mutually exchanged. In this case, as the resistance value seenfrom the input terminals 29 and 30, a negative resistance may berealized. Moreover, in the embodiment in FIG. 10, the transistors Q₉ andQ₁₀ are used as the resistive load of the transistors Q₁ and Q₂, but itis also possible, needless to say, to use an ordinary resistance elementas shown in FIG. 2.

Thus, according to the embodiment shown in FIG. 10, the resistance valuecan be changed in a broader range than the variation of the differentialemitter resistance of a transistor, and the variable range of theresistance value can be freely changed by changing the current value ofthe current source connected to the transistor pair of the differentialamplifier circuit.

FIG. 11 relates to an eighth embodiment of the invention. In FIG. 11,variable capacitance circuits 100, 101, substantially equivalent to thecomposition shown in FIG. 2, are connected in cascade. A capacitanceelement 33 is connected between the emitters of the transistors Q₁, Q₂for composing the differential amplifier circuit 1 of the variablecapacitance circuit 101. The capacitance value of this capacitanceelement 33 is supposed to be C₂. The resistance value of the resistanceelement 34 connected to the base of the transistor Q₁ of the variablecapacitance circuit 100 is supposed to be R₃₄, and the resistance valueof the resistance element 35 connected between the reference potentialand the base of the transistor Q₂ of the variable capacitance circuit100 is supposed to be R₃₅. The rest of the composition is the same as inFIG. 2.

This embodiment is intended to obtain a large (infinite, theoretically)capacitance on the basis of the following principle.

Supposing the capacitance values of two capacitance elements to be-C_(A), C_(B), and the synthetic capacitance by connecting them inseries to be C, the following relation is obtained. ##EQU28## Therefore,it follows that ##EQU29## and when C_(A) =C_(B), C is infinite.Generally, in a semiconductor integrated circuit, since the relativeprecision of elements is extremely high, when the circuit is designed sothat, for example, C_(A) =1.01 C_(B), C is ##EQU30## and a capacitancevalue of over 100 times will be easily capacitance obtained. By the sameprinciple, a negative capacitance may be realized.

Next, according to the composition shown in FIG. 11, its operation isexplained below.

Supposing the base AC voltage of the transistor Q₁ of the variablecapacitance circuit 100 to be V_(o), and the base AC voltage of thetransistor Q₂ to be V_(b), they are ##EQU31## Here, assuming the twovariable capacitance circuits 100, 101 to be symmetrical, and R₂ =R₃,from equations (45), (46), it follows that ##EQU32## Putting equation(47) into equation (45) yields ##EQU33## From equation (48), it is foundthat ##EQU34## Therefore, when C₁ =C₂, Q is infinite, and a secondarylow pass filter with an extremely high selectivity will be realized.

On the other hand, when the resistance value R₃₅ is an extremely largevalue, it results in ##EQU35## Hence, when C₁ =C₂, a primary low passfilter having 35 equivalently an extremly large capacitance value##EQU36## may be realized.

Along with the advancement in the degree of integration of thesemiconductor integrated circuit, it is demanded to incorporate externalparts, in particular, capacitance elements with large capacitance valueinto a semiconductor chip. Generally, in a semiconductor integratedcircuit, the relative precision of elements, such as capacitors,resistors and transistors is extremely high, and therefore it is quiteeasy to set the capacitance values C₁, C₂ of the two capacitanceelements 3 and 33 in FIG. 11 nearly equal to each other (for example, C₁=1.01 C₂). Therefore, hitherto, within the semiconductor chip, it wasbound to realize a capacitance value of only about 100 pF from aneconomical point of view, while, by contrast, in the composition asshown in FIG. 11, an extremely large capacitance value may be realizedin a semiconductor integrated circuit.

We claim:
 1. A variable impedance circuit comprising:a firstdifferential amplifier circuit having an input terminal pair, an outputterminal pair and impedance element connected between emitters of atransistor pair; a second differential amplifier circuit having an inputterminal pair and an output terminal pair; means for connecting saidoutput terminal pair of said first differential amplifier circuit tosaid input terminal pair of said second differential amplifier circuit;means for connecting said output terminal pair of said seconddifferential amplifier circuit to said input terminal pair of said firstdifferential amplifier circuit; and, a resistance element connectedbetween said input terminal pair of said second differential amplifiercircuit.
 2. A circuit as recited in claim 1, said impedance elementbeing a capacitive element.
 3. A circuit as recited in claim 2, furthercomprising a resistive element connected between emitters of atransistor pair of said second differential amplifier circuit.
 4. Acircuit as recited in claim 1, further comprising a resistive elementconnected between emitters of a transistor pair of said seconddifferential amplifier circuit.
 5. A variable impedance circuitcomprising:a first differential amplifier circuit having an inputterminal pair, an output terminal pair and an impedance elementconnected between emitters of a transistor pair; a second differentialamplifier circuit having an input terminal pair and an output terminalpair; means for connecting said output terminal pair of said firstdifferential amplifier circuit to said input terminal pair of saidsecond differential amplifier circuit; means for connecting said outputterminal pair of said second differential amplifier circuit to saidinput terminal pair of said first differential amplifier circuit; and, aresistance element connected between said input terminal pair of saidfirst differential amplifier circuit.
 6. A circuit as recited in claim5, said impedance element being a capacitive element.
 7. A circuit asrecited in claim 6, further comprising a resistive element connectedbetween emitters of a transistor pair of said second differentialamplifier circuit.
 8. A circuit as recited in claim 5, furthercomprising a resistive element connected between emitters of atransistor pair of said second differential amplifier circuit.
 9. Avariable impedance circuit comprising:a first differential amplifiercircuit having an input terminal pair, an output terminal pair and animpedance element connected between emitters of a transistor pair; asecond differential amplifier circuit having an input terminal pair andan output terminal pair; means for connecting said output terminal pairof said first differential amplifier circuit to said input terminal pairof said second differential amplifier circuit; means for connecting saidoutput terminal pair of said second differential amplifier circuit tosaid input terminal pair of said first differential amplifier circuit;and, said impedance element being a capacitive element.
 10. A circuit asrecited in claim 9, further comprising a resistive element connectedbetween emitters of a transistor pair of said second differentialamplifier circuit.
 11. A variable impedance circuit comprising:a firstdifferential amplifier circuit having an input terminal pair, an outputterminal pair and an impedance element connected between emitters of atransistor pair; a second differential amplifier circuit having an inputterminal pair and an output terminal pair; first means for connectingsaid output terminal pair of said first differential amplifier circuitto said input terminal pair of said second differential amplifiercircuit; second means for connecting said output terminal pair of saidsecond differential amplifier circuit to said input terminal pair ofsaid first differential amplifier circuit; and, said second meansincluding a current-current circuit comprising (a) a third differentialamplifier circuit having an output terminal pair connected to said inputterminal pair of said first differential amplifier and an input terminalpair connected to said output terminal pair of said second differentialamplifier, (b) a constant current source connected to a common emitterof said third differential amplifier circuit, and (c) a transistor pairrespectively connected between each of said output terminal pair of saidsecond differential amplifier and a reference potential.
 12. A variableimpedance circuit comprising:a first differential amplifier circuithaving an input terminal pair, an output terminal pair and an impedanceelement connected between emitters of a first transistor pair; a seconddifferential amplifier circuit having an input terminal pair and anoutput terminal pair and a second transistor pair; means for connectingsaid output terminal pair of said first differential amplifier circuitto said input terminal pair of said second differential amplifiercircuit; means for connecting said output terminal pair of said seconddifferential amplifier circuit to said input terminal pair of said firstdifferential amplifier circuit; a constant current source connectedbetween a common emitter of said second transistor pair of said seconddifferential amplifier circuit and a first voltage source; a thirdtransistor pair respectively connected between each input terminal pairof said second differential amplifier circuit and said first voltagesource; and, a second voltage source being connected as a base bias toeach of said third transistor pair.
 13. A variable impedance circuitcomprising:a first differential amplifier circuit having an inputterminal pair, an output terminal pair and a first impedance elementconnected between emitters of a transistor pair; a second differentialamplifier circuit having an input terminal pair and an output terminalpair; means for connecting said output terminal pair of said firstdifferential amplifier circuit to said input terminal pair of saidsecond differential amplifier circuit; means for connecting said outputterminal pair of said second differential amplifier circuit to saidinput terminal pair of said first differential amplifier circuit; athird differential amplifier circuit having an input terminal pair, anoutput terminal pair and an impedance element connected between emittersof a transistor pair; a fourth differential amplifier circuit having aninput terminal pair and an output terminal pair; means for connectingsaid output terminal pair of said third differential amplifier circuitto said input terminal pair of said fourth differential amplifiercircuit; means for connecting said output terminal pair of said fourthdifferential amplifier circuit to said input terminal pair of said thirddifferential amplifier circuit; and, means for connecting one of saidinput terminal pair of said first differential amplifier circuit to oneof said input terminal pair of said third differential amplifiercircuit.